This invention relates to nuclear magnetic resonance (NMR) imaging methods and apparatus and more particularly to a method of reducing image artifacts caused by truncation of the NMR data along one or more k-space axes.
NMR has been developed as an imaging method useful in diagnostic medicine. In NMR imaging, as is understood by those skilled in the art, a body being imaged is held within a uniform magnetic field oriented along a z axis of a Cartesian coordinate system.
The net magnetizations of the nuclei of the body are excited into precession by means of a radio frequency (RF) pulse and the decaying precession of the spins produces an NMR signal. The amplitude of the NMR signal is dependant, among other factors, on the number of precessing nuclei per volume within the imaged body termed the "spin density".
Magnetic gradient fields G.sub.x, G.sub.y, and G.sub.z are applied along the x, y and z axis to impress position information onto the NMR signals through phase and frequency encoding. A set of NMR signals may then be "reconstructed" to produce an image. Each set of NMR signals is comprised of many "views", a view being defined as one or more NMR signal acquisitions made under the same x and y gradients fields.
One NMR image reconstruction technique, associated with "spin warp" imaging, will be described herein. It should be recognized however that the present invention may be advantageously practiced with other NMR image acquisition techniques.
Referring to FIG. 1, a typical "spin echo" pulse sequence for acquiring data under the spin warp technique includes: (1) a z-axis gradient G.sub.z activated during a first 90.degree. RF pulse to select the image slice in the z axis, (2) a y-axis gradient field G.sub.y to phase encode the precessing nuclear spins in the y direction, and (3) an x-axis gradient G.sub.x activated during the acquisition of the NMR signal to frequency encode the precessing nuclear spins in the x direction. The time during which steps (1) and (2) are performed will be termed the "encoding interval" 11 and the time during which step 3 is performed will be termed the "acquisition interval" 13.
Two such NMR acquisitions, S.sub.1 and S.sub.1 ', the latter inverted and summed with the first, comprise the NMR signal of a single view "A" under this sequence Note that only the y gradient field G.sub.y changes between view "A" and subsequent view "B". This pulse sequence is described in detail in U.S. Pat. No. 4,443,760, entitled: "Use of Phase Alternated RF Pulses to Eliminate Effects of Spurious Free Induction Decay Caused by Imperfect 180 Degree RF Pulses in NMR Imaging", and issued Apr. 17, 1984.
Referring to FIG. 2, the acquisition of a plurality of NMR signals to construct an image is illustrated by referring to the concept of k-space. An imaged object 10 is subject to the pulse sequence of FIG. 1. The NMR signals comprising one view provides the data elements 16 within a bounded area of k-space 12 along one "row" 14 of k-space 12 orientated along the k.sub.x axis. Each data element 16 of the row 14, is a sequential sample of the NMR waveforms produced by the pulse sequence for that view. The particular row 14 of the view is determined by the relative amplitude of G.sub.y for that NMR signal acquisition: for example, more positive gradients G.sub.y (each measured by area) will produce the NMR signals filling higher rows. The process of acquiring data to fill the rows of k-space will be termed "scanning".
During the scanning process, additional rows of the bounded k-space area 12 are filled by repeated NMR signal acquisitions at different gradients G.sub.y. The data elements 16 of the k-space area 12 are then subject to a two-dimensional Fourier transform along the k.sub.x and k.sub.y axes to produce the image 18.
Within k-space, data close to the origin 20 contains the low frequency spatial components of the image 18 and data removed from the origin contains the high frequency spatial components of the image 18. It may be understood, therefore, that the dimensions of k-space correspond to the resolution of the image 18; data filling a larger area of k-space generally produces an image containing higher frequency components and hence higher spatial resolution.
While resolution of the image is important, practical limits on the scanning time, which may be on the order of several minutes per slice, require that the area of k-space filled with data be limited.
The total scanning time needed to acquire data 16 is most sensitive to the number of rows 14 of k-space data, hence the height of columns of k-space data, and less sensitive to length of each row 14 of data. The reason for this may be illustrated by referring to FIG. 1. The time required to acquire data for a k-space row 14 is the sum of the encoding interval 11 plus the acquisition interval 13 (times two for the spin echo sequence shown). Decreasing the length of a k-space row, decreases the acquisition interval 13 but not the encoding interval 11. Thus the savings of time resulting from decreasing the length of the k-space row 14 is diminished by effect of the fixed encoding interval 11.
On the other hand, decreasing the number of rows 14 of k-space data eliminates the encoding and acquisition intervals 11 and 13 associated with those rows 14 and hence has a more profound effect on the total scanning time. For this reason, it is desirable that the number of rows of k-space data acquired be limited to the number necessary for clinically acceptable resolution.
The acquisition of a reduced field of data in k-space will be termed "truncation". Referring to FIG. 3, a truncated projection 12' includes a limited number of k-space rows centered about the origin 20. In contrast to the projection set 12 shown in FIG. 2, the outer rows of k-space have not been filled. The area of these outer rows will be designated Regions 1 and 3, whereas the area of k-space in which data is acquired will be designated Region 2.
Although the reduced spatial resolution resulting from the truncation process may be acceptable, the truncation process also produces truncation artifacts. Referring to FIG. 4(a), an example non-truncated NMR signal 21 from a single column of k-space 12 is shown. The Fourier transform of the signal 21 is a step function 22, shown in FIG. 4(b), and corresponding to an "edge" 24 between light and dark areas of image 18.
Referring to FIG. 4(c), the truncation process is equivalent to multiplying the non-truncated signal 21 by a rectangular truncation function 26 which has a value of "one" for values of k.sub.y corresponding to Region 2 of FIG. 3 and values of "zero" for values of k.sub.y corresponding to Regions 1 and 3 of FIG. 3. The rectangular truncation function has a Fourier transform that is a sinc function 28, as shown in FIG. 4(d).
The image produced by the truncated data will be the Fourier transform of the product of the non-truncated data 21 and the rectangular truncation function 26. This is equivalent to the convolution of the Fourier transforms 24 and 28 as shown in FIGS. 4(b) and 4(d). The result of this convolution is shown in FIG. 4(e). The convolution 30 preserves the edge 24 of the step function 22 of FIG. 4(b) but includes ripple truncation artifacts caused by the lobes of the sinc function 28. The most prominent truncation artifact 32 is a result of the primary lobe of the sinc function 36.
As the truncation becomes more severe, i.e., the rectangular truncation function 26 becomes narrower, the truncation artifact ripples 32 become spaced further from the edge 24, but nevertheless maintain the same amplitude of approximately 9% of the height of the step function 22. In the image 18, the truncation artifacts appear as halos extending along the axis of truncation around edges 24 in the image 18.
Thus, even if the truncated projection set provides acceptable spatial resolution, the truncation may produce unacceptable truncation artifacts.
Truncation artifacts may be removed by low-pass filtering of the projection data, however, this produces a corresponding and severe loss of image resolution.
Alternatively, it has been recognized that truncation artifacts may be reduced by recreating the high frequency data removed as a result of the truncation process. Such methods currently attempt to extrapolate the high frequency data of Regions 1 and 3 through the use of linear predictive models operating directly on the data of Region 2.